This is how I rooted stock MK3 on Sprint. Read the instructions carefully. The trick for me was to go to the play store once I was done and re-install or upgrade SuperSU, then run it.
I am now on MK3, rooted.
Novatel Bagphone, Motorola Microtac, Qualcom Q-Phone, Motorola Startac, Sanyo MM-8100, Sanyo MM7400, Samsung A900 Blade, HTC Touch Pro 2, Sammy Epic 4G,
Currently Sammy Galaxy S III running Stock Rooted KitKat 4.4.2 because it's just that good. Knox don't scare me
Sprint SERO Premium 500